Download Cell assemblies in the cerebral cortex Günther Palm, Andreas

Cell assemblies in the cerebral cortex
Günther Palm, Andreas Knoblauch,
Florian Hauser & Almut Schüz
Biological Cybernetics
Advances in Computational
Neuroscience
ISSN 0340-1200
Biol Cybern
DOI 10.1007/s00422-014-0596-4
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DOI 10.1007/s00422-014-0596-4
PROSPECTS
Cell assemblies in the cerebral cortex
Günther Palm · Andreas Knoblauch ·
Florian Hauser · Almut Schüz
Received: 31 May 2013 / Accepted: 27 February 2014
© Springer-Verlag Berlin Heidelberg 2014
Abstract Donald Hebb’s concept of cell assemblies is a
physiology-based idea for a distributed neural representation
of behaviorally relevant objects, concepts, or constellations.
In the late 70s Valentino Braitenberg started the endeavor to
spell out the hypothesis that the cerebral cortex is the structure where cell assemblies are formed, maintained and used,
in terms of neuroanatomy (which was his main concern) and
also neurophysiology. This endeavor has been carried on over
the last 30 years corroborating most of his findings and interpretations. This paper summarizes the present state of cell
assembly theory, realized in a network of associative memories, and of the anatomical evidence for its location in the
cerebral cortex.
Keywords Cerebral cortex · Cell assemblies · Synaptic
plasticity · Associative memory · Brain theory
This article forms part of a special issue of Biological Cybernetics entitled “Structural Aspects of Biological Cybernetics: Valentino Braitenberg, Neuroanatomy, and Brain Function”.
G. Palm (B)· F. Hauser
Institute of Neural Information Processing, University of Ulm,
89069 Ulm, Germany
e-mail: [email protected]
A. Knoblauch
Honda Research Institute Europe GmbH, Offenbach/Main,
Germany
A. Knoblauch
Engineering Faculty, Albstadt-Sigmaringen University,
72458 Albstadt , Germany
A. Schüz
MPI for Biological Cybernetics,
72076 Tübingen, Germany
1 Introduction
“To say that an animal responds to sensory stimuli may not
be the most natural and efficient way to describe behaviour.
Rather, it appears that animals most of the time react to situations, to opponents or things which they actively isolate
from their environment. Situations, things, partners or opponents are, in a way, the terms of behaviour. It is legitimate,
therefore, to ask what phenomena correspond to them in the
internal activity of the brain, or, in other words: how are the
meaningful chunks of experience ‘represented’ in the brain?
A crude version of this question takes the form: is the
presence of a relevant happening signaled by the activity
of just one neuron, which otherwise is always silent, or is
it represented by an irreducibly complex description of the
activity of the brain?
Following an old idea (Hebb 1949 and older) we shall
explore the possibility that it is neither single neurons nor
abstract diffuse properties of the state of the brain which
correspond to the relevant events of behaviour, but something
in between, identifiable sets of neurons.
These ‘cell assemblies’ have recently gained support from
neurophysiology in two ways. First, many years of recording
responses of single neurons to sensory stimuli have shown
that no very complicated or very unique input is needed
to activate a neuron. The most efficient stimuli for cortical
neurons are rather elementary configurations of the sensory
input, such as moving lines in narrow regions of the visual
field (Hubel and Wiesel 1959) or changing frequencies in
certain delimited regions of the acoustic spectrum (Evans
1968). These ‘features’ cannot independently carry meaning but must be in the same relation to meaningful events
as the phonemes of linguistics are to words or sentences.
The whole meaningful event must be signaled in the brain
by a set of neurons, each contributing a particular aspect
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which that event may have in common with many other
events.
The second line of evidence is derived from the neurophysiology of learning. It was one of Hebb’s points that cell
assemblies representing things in the brain are held together
by excitatory connections between the neurons of which
they are composed, and that these connections are established through a learning process. The most natural way in
which such learning could take place is if a statistical correlation, say, a frequent coincidence of a certain set of elementary features in the input were transformed into synaptic connections between the corresponding neurons. Some
recent observations on the plasticity of the connections of
single neurons (Hubel and Wiesel 1965; Wiesel and Hubel
1965; Blakemore and Cooper 1971; Hirsch and Spinelli
1971) can indeed be explained by invoking such a mechanism.
It seems timely, therefore, to reconsider cell assemblies as
a possible substrate of behaviour, and, particularly, to review
the cerebral cortex with the idea in mind that it might be the
place where cell assemblies are formed and sustained.
There remains one nagging thought, however, when we
dismiss single neurons as the elements onto which complex situations, things, etc. are mapped in the brain. Suppose we were recording with a microelectrode from a neuron whose activity corresponds exactly to the presence of a
close relative or to a particular bird’s song, or to the memory of a particular scent. The probability that, while we are
recording we stumble accidentally upon such very rare stimulus configurations is negligibly small. Thus, strictly speaking, the idea of single neurons as classificatory elements for
complex situations is beyond proof or disproof. Of course
for similar reasons and for added technical difficulties it
is even more hopeless to expect experimental proof of the
correspondence of a cell assembly to a certain event in the
input. In this field we must rely on theoretical plausibility
and on considerations about the structure of networks in
the brain that may seem more suited for one or the other
scheme.”
Valentino Braitenberg wrote this beautiful introduction to
his article on this subject in 1978. Here we want to spell out
some of these old ideas about cell assemblies in the cortex
in more detail in the light of the neuroscientific advances in
the last 30 years.
In a nutshell, it turns out that most of the ideas presented
in Valentino’s article have been substantiated and sometimes
specified more clearly by this research, and only very few
have to be revised.
In a very general formulation these are the main points:
1. Most of the input to cortical neurons comes from other
cortical neurons, i.e. the cortex works mostly on its own
output.
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2. There is an informational imbalance between excitation
and inhibition since excitatory connections greatly outnumber inhibitory ones.
3. The global cortico-cortical feedback is positive, since
cortico-cortical fibers are excitatory.
4. There is a great dispersion of information in the cortical
connectivity system .
5. Cortical connectivity can be described as the cooperation
of an A- and a B-system, where the A-system distributes
information globally by cortico-cortical fibers and the
B-system distributes information locally by intracortical
axonal arborizations.
6. There is a predominance of inborn specificity in the
wiring at the macro-level (e.g. in the connection of areas)
and of randomness (or individuality) at the micro-level.
7. Synaptic plasticity in the cortex is predominantly of the
Hebbian type, i.e. excitatory synapses are strengthened
by coincident firing of the pre- and postsynaptic neurons.
Now we will spell out these points in more detail also considering some of their further developments and functional
consequences.
Building on Hebb’s original, mostly representational arguments for cell assemblies, the further development of cell
assembly theory was mainly driven by neurophysiological and biophysical findings concerning the basic neuronal
mechanisms and the detailed temporal processes of neuronal
activation and interaction on one hand and by computational
arguments and requirements on the other.
The neuroanatomical aspects are discussed in the next
Sect. 2. Functional consequences of Braitenberg’s points in
terms of a theory of cortical cell assemblies and its development from 1977 to the present time are detailed in the following sections. Section 3 describes the underlying network
structure and Sect. 4 the ongoing computational process in a
simplified abstract way. Section 5 considers the further development of Hebbian synaptic plasticity, i.e. its fine temporal
aspects.
2 Results from neuroanatomy
As mentioned in Braitenberg’s introduction, Hebb based his
theory on excitatory synaptic connections: he assumed that
neurons which are repeatedly active together become more
strongly connected, an idea which Hebb himself mentions
to be “an old idea”. In this way, correlations in the outside
world, such as the different properties of an object, can be
inscribed into the brain. As a result, cell assemblies will be
formed which are more strongly connected among each other
than with other neurons. Braitenberg then elaborates in more
detail on the consequences of mutual excitation, such as the
ignition of an assembly when only some of its members are
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activated, or the possibility of associations between different
cell assemblies.
An important argument in Braitenberg’s 1978-paper in
support of the Hebbian theory was therefore the assumption
that pyramidal cells, being the main cell type in the cortex,
are excitatory neurons (points 2 and 3 above). He presents
the arguments in favour of this, but it is interesting to see that
this was not yet entirely certain at the time. In the meantime
this is a fact beyond doubt, shown directly in many electrophysiological studies (e.g. Miles and Wong 1986; Thomson
and Deuschars 1994; Markram et al. 1997).
The prevalence of excitatory connections has also been
confirmed directly since then by showing that not only in
the cerebellar (Uchizono 1965), but also in the cerebral cortex (e.g. Houser et al. 1984), synapses with a symmetrical
appearance in the electron microscope contain the inhibitory
transmitter GABA. These so-called Type-II synapses were
known to constitute only a minority of the synapses in the
cerebral cortex (e.g. Gray 1959; Colonnier 1968; Peters and
Feldman 1976; Wolff 1976; Bär 1977).
These and many other structural properties have been
quantified in the following years in the mouse cortex, as well
as in other species (For reviews see White 1989; Braitenberg
and Schüz 1991, 1998; DeFelipe et al. 2002). These studies
provided further support for the theory of cell assemblies;
they showed that the structure of the cortex (including the
hippocampus) fully satisfies the requirements for this theory, in contrast to the structure of other main parts of the
brain (cerebellar cortex, basal ganglia, thalamus). The cerebral cortex is the only large network in the brain which consists mainly of excitatory connections within itself (points
1–3). In addition, these connections are highly divergent and
convergent (point 4) and thus allow for a rich repertoire of
correlations and associations,as required for this theory.
Braitenberg’s point 4 has been substantiated during the
last decades by the large amount of studies with anterograde
and retrograde tracers in rodents, cats and primates, showing
the connectivity between cortical areas. Many of the data in
cats and/or monkeys have been summarized by Young et al.
(1995) and in the database CoCoMac initiated by Rolf Kötter
(Stephan et al. 2001; Kötter 2004; Bakker et al. 2012). It can
be seen, for example, that many cortical areas in the monkey
are connected with more than 10 other cortical areas.
The high degree of divergence and convergence becomes
even more evident if one quantifies the density of fibers in
terminal fields coming from a given injection site, as has
been done in a tracer study in the mouse cortex. It could
be shown that the axonal branches from an injection site
comprising many thousand neurons contribute only a few
percent to the total axonal density in the surrounding local
terminal field, and they contribute even less than one percent
to the axonal density in a distant projection field (Schüz et al.
2006). Thus, many terminal fields from both local and distant
Fig. 1 Estimate of the number of fibers N (in both hemispheres
together) connecting the human neocortex within itself in its horizontal plane (log–log plot). Compartment A population of axon collaterals
of pyramidal cells running tangentially within the grey matter over a
few millimeters, based on an estimate of five horizontal collaterals per
pyramidal cell. Compartment B U-fiber system, connecting the cortex
within itself over a few centimeters. Compartment C all cortico-cortical
fibers of longer range, running in the depth of the white matter, i.e. fibers
which make short-cuts between folds within the same lobe, fibers which
connect the different lobes with each other and fibers of the Corpus callosum. From: Schüz and Braitenberg (2002), with permission
regions have to converge at any given place in order to arrive
at the total density of axons in the cortex of about 4 km/mm3
(Braitenberg and Schüz 1998).
Another interesting fact shown by these numbers in the
mouse is the quantitative dominance of shorter connections
(i.e. within an area and between neighbouring areas) over
longer ones. This seems to be a general feature in both, small
and large brains. Although areas far away from each other
can be connected, nearly half of the interareal connections
are nearest-neighbour or next-door-but-one connections as
has been shown by Scannell et al. (1995) for the cat. A finding in human brains goes into the same direction (Schüz and
Braitenberg 2002): there is an inverse relationship between
number and length of fibers connecting the cortex in its horizontal plane (Fig. 1).
For the division into a global and a local connectivity system (point 5), Braitenberg used the term A (apical) and B
(basal) system, respectively, in view of the fact that often
cortico-cortical inputs from other areas project into upper
layers and reach there also the neurons from the lower layers
via their apical dendrites. Nowadays one knows that this projection pattern is not general for all cortical areas; for example, in sensory areas it concerns only the feedback connections from hierarchically higher to lower areas (e.g. Rockland
and Pandya 1979; Rockland and Virga 1989; Cauller 1995;
Rockland 2004).
In addition to a local and a global connectivity system
one needs also to include a middle range system in order
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to do justice to the connectivity in large brains. An indication for this are the horizontal stripes of myelinated fibers
within the gray matter which were known in the human cortex since the times of Gennari (1782) and Baillarger (1840)
and which contributed to the myeloarchitectonic differentiation of cortical areas (e.g. Vogt and Vogt 1919; for review see
Nieuwenhuys 2013). Braitenberg himself spent some time in
the Vogts’ laboratory in the 1950s and was attracted by myeloarchitectonics as an expression of differences in the wiring
diagrams of the various cortical areas. He provided evidence
for the assumption that these stripes correspond to the axon
collaterals of pyramidal cells located in the layers above the
stripes (Braitenberg 1962). This was later substantiated by
Hellwig (1993) who showed how myeloarchitectonics can
be generated from cyto-architectonic pictures. It is interesting to see the recent relevance of this old research in connection with current approaches to in-vivo-imaging of cortical
myeloarchitectonics (Bock et al. 2013; Nieuwenhuys 2013).
Knowledge about this middle range system has increased
considerably during the last two decades. It could be shown
that the long horizontal collaterals in the gray matter give
off patchy ramifications over a region of several millimeters, usually within the same area, and that the lateral spread
increases with hierarchy of sensory cortical areas (e.g. Amir
et al. 1993; Levitt and Lund 2002; Voges et al. 2010).
Quite a number of studies have dealt with the question
of randomness of connectivity on the micro level (point
6), constrained by the geometry of axonal and dendritic
arborizations. This assumption is still a successfully used
first approach to understand connectivity (e.g. Binzegger
et al. 2004) or—expressed more cautiously by Stepanyants
and Chklovskii 2005)—potential connectivity in the cortex.
Knowledge about the particular geometry of neurons in different layers gained by Golgi studies over the last century
has further increased during the last decades by using intracellular injections of neurons (e.g. Binzegger et al. 2004;
Stepanyants et al. 2008) and with it knowledge about the
connectivity between layers and cell types (e.g. Binzegger
et al. 2007). Electron microscopical studies have confirmed
randomness of connectivity in some pyramidal cell systems,
but have also shown biases away from randomness in some
others (for an overview see White 1989; Braitenberg and
Schüz 1998). Physiological investigations have also shown
some interesting deviations from the anatomically expected
connectivity scheme in case of subtypes of inhibitory neurons (Dantzker and Callaway 2000). A comprehensive review
of such investigations and a heroic effort to understand the
complex relation between anatomical and physiologically
explored data on connectivity has been presented by Potjans
and Diesmann (2012).
At the end of this section we want to come back to the
“nagging thought” in Braitenberg’s introduction, i.e. the difficulty or even the potential impossibility to prove or dis-
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prove the representation of events in terms of cell assemblies as opposed to single neurons empirically. Indeed, today
there may be hope: the fascinating technical developments in
the field of multiphoton-microscopy and genetically encoded
calcium indicators make it now possible to visualize the activity of neuronal populations on the single cell level and over
long periods of time. They have opened up the possibility to
relate the activity of neuronal populations to behaviour (for
reviews see Kerr and Denk 2008; Wallace and Kerr 2010).
Furthermore, in a recent study on the hippocampus Liu et
al. (2012) were able to induce fear behaviour by optogenetic
stimulation of neurons which had been activated during learning of this behaviour, indicating that these neurons were part
of the engram leading to this behaviour. Thus, new insights
into the representation of events will be possible which could
hardly be foreseen at the time when Valentino wrote his article. In addition, new computational methods have been developed that alleviate the combinatorial problem of identifying
correlation structures involving several neurons (i.e. more
than two) in multi-unit recordings (see Picado-Muino et al.
2013).
3 Global cortical asssemblies
The view of the cerebral cortex as a substrate for Hebbian
cell assemblies formed by associative memory mechanisms,
i.e. Hebbian synaptic plasticity, was certainly the first point
of Valentino’s article. It is consistent with the anatomical
observations summarized in the introduction. In particular,
the stabilization of cell assemblies by auto-association, a cornerstone of cell assembly theory, requires a prominence of
excitatory connections between cortical neurons that are further strengthened by Hebbian synaptic plasticity (points 2, 3,
7). However, there is an additional component in Valentino’s
assembly concept, namely that at each moment in time there
is only one assembly active in the whole cortex. This view
is motivated by the subjective unity of conscious experience
and by the idea that the cortex combines all the incoming
information from different sensory systems and proprioceptors with the reafference of the motor commands into one
coherent representation of the present situation. This idea
is substantiated by the anatomical evidence for rich excitatory interconnectivity by the combination of intra-cortical
and cortico-cortical connections (points 4, 5).
In his article Valentino goes on to describe the advantages of a cell assembly representation consisting of many
neurons distributed all over the cortex versus the naive one
“grandmother” neuron representation, and he also speculates
about the dynamics of the activation of assemblies in terms
of “threshold control”, i.e. of global activation or inhibition
of all pyramidal cells in larger regions of the cortex. In this
context the formation, detection and production of sequences
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of assemblies (corresponding to Hebb’s “phase sequences”)
was also discussed and even the possibility of a fast temporal structure inside the activation of one assembly was
mentioned, but not spelled out in detail. These two levels
of temporal structure can be understood as the first stages of
a hierarchical temporal structure, which was considered to
be functionally meaningful for example in the representation
and parsing of language, as mentioned already in Valentino’s
1978 article. The idea of sequencing and/or fine temporal
structures of assemblies has been elaborated in particular
by (Abeles 1982, 1991), who presented evidence for precise
temporal events in multi-unit spike trains which could be
explained by hetero-associative temporal structure in assemblies, also called “synfire-chains”. The early ideas concerning assembly dynamics, fine temporal structure, and temporal hierarchies probably needed the most extensive elaboration from a neurophysiological point of view. This has
indeed been developed by several authors until the present
time (e.g.Bienenstock 1995; Thorpe et al. 1996; Wennekers
1998, 2006; Miller 2000; Rullen and Thorpe 2001; Rao 2005;
Izhikevich and Hoppensteadt 2009; Szatmáry and Izhikevich
2010; Humble et al. 2012). Also a more detailed modeling of
the 6-layered intra-cortical connectivity structure has been
incorporated into assembly theory (e.g. Krone et al. 1986;
Hawkins and Blakeslee 2004, see also Potjans and Diesmann 2012). In his book “Neural Assemblies. An Alternative
Approach to Artificial Intelligence” Palm (1982a) developed
a more detailed computational view of the practical use of
cell assemblies in the cortex for solving various problems
that may help the animal to survive. This involves speculations about prediction, generating sequences, planning
actions, delayed reward and reinforcement learning (Sutton
and Barto 1998; Russel and Narvig 2003), hierarchies and
many other ideas from the then relatively new field of artificial intelligence (Winston 1984).
These early ideas have been extended in many directions by Valentino’s scholars, including the authors of this
article (see Palm 1987b, 1990a, 1993b; Krone et al. 1986;
Abeles 1988; Schüz and Palm 1989; Braitenberg and Schüz
1991; Wennekers et al. 1995,Wennekers and Palm 19986
Knoblauch and Palm 2001, 2002a,b; Pulvermüller 2002;
Schüz and Braitenberg 2002; Knoblauch et al. 2005a,b; Wennekers 2006; Markert et al. 2007; Wennekers and Palm 2007;
Kiefer and Pulvermüller 2012; Shtyrov et al. 2012) Similar ideas have of course also been presented by many other
authors during the last 30 years (e.g. Miller 1996; Hawkins
and Blakeslee 2004; Rao 2005; Hecht-Nielsen 2007; Lansner
2009 and authors in Aertsen 1993). One important conceptual point in our further development of assembly theory is
to view the cortex not just as one big associative memory, but
as a network of interconnected local memories. According
to the view already sketched by Palm (1990a, 1993a) and
elaborated for example by Knoblauch et al. (2005a,b) and
Bouchain and Palm (2012), each local “node” in this network can be considered as a piece of cortex ranging in size
from a “hypercolumn” (Hubel and Wiesel 1974, 1977, i.e.
about 1 mm2 surface area) to a small “cortical area” (perhaps
up to 50 mm2 ). In reality such a node or “module” cannot be
regarded as a well-separated piece of cortex, but is locally
connected to the neighboring nodes. Basically each local
cortical “column” is connected to its neighborhood with a
connection density that decreases continuously with distance
perhaps up to a millimeter (in addition to a few millimeters
of patchy intra-areal connections that have been observed in
some species such as cats and primates).
In our view such a node consists of two associative memories: an auto-associative one, where the local activity patterns are stored or stabilized by Hebbian learning (Braitenberg’s B-system) and a hetero-associative one (Braitenberg’s
A-system) which learns associations between activation patterns of some other cortical areas that are transmitted to the
local node by cortico-cortical fiber connections and the currently active local pattern. These hetero-associative memories can be used to match the local activation with the incoming activation from other areas yielding strong local activation when everything fits together and weaker activation
down to local inactivation if the patterns don’t fit so well.
Qualitatively, such a view of the prevalent cortical computation is shared by most of the popular “brain theories” that have
been proposed over the years (e.g. Legéndy 1967, 1975; Marr
1969, 1970, 1971; Palm 1982a; Palm and Aertsen 1986; Amit
1989; Bienenstock 1995; Grossberg 1976a,b, 1982, 1999;
Rao and Ballard 1999; Edelman and Tononi 2000; Hawkins
and Blakeslee 2004; Anderson 2004; Hecht-Nielsen 2007;
George and Hawkins 2009; Eliasmith 2013), although the
verbal descriptions all use different terminology. An interesting exception seems to be the view proposed by Dana
Ballard and some of his pupils. Here again the local activity
is matched against the incoming signals from other areas,
but the resulting local activity and also the output activity
from the local node measures the difference (or dissonance)
between the local and global activities, which may also be
viewed as the “prediction error”, instead of the degree of
agreement (or consonance). In spite of this clear conceptual
difference it is not at all easy to discriminate these two views
experimentally. Perhaps some of the cortical areas adhere to
Dana’s principle and most others to ours, or perhaps many
areas can somehow even do both? This last view is detailed in
a paper by Knoblauch et al. (2007), where the idea is, roughly
speaking, that consonance is the dominant mode of operation
and only cortical layer III works according to the difference
principle. This model also offers the possibility to reconcile
apparently conflicting experimental evidence on this issue.
Our global assembly theory also seems to be generally consistent with some very detailed cortical models of the visual
system (e.g. George and Hawkins 2009; Weidenbacher and
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Neumann 2009; Raudies and Neumann 2010; Poort et al.
2012) and therefore can serve as a framework for embedding
these models into a unified global brain theory.
One specific point distinguishing our view from most of
the other theories is derived from a mathematical analysis of
the efficiency of associative memories that are based on Hebbian synaptic plasticity: the stored activity patterns, i.e. the
local assemblies in each of the local nodes have to be sparse,
i.e. only a very low fraction of the local neurons should be
active (Palm 1980, 1987a, 1990b, 2013; Palm and Sommer
1992; Palm et al. 1994; Markert et al. 2008; Knoblauch et al.
2010; Knoblauch 2011). This sparseness requirement seems
to fit well to neurophysiological observations (e.g. Waydo et
al. 2006).
Since we don’t know which of the current “brain theories”
are true, and they are not easy to distinguish, anyway, one
reasonable strategy that we are following now is to see how
far we can get with the machinery proposed here, i.e. with a
network of associative memories.
4 Computation in associative networks
In order to understand the computational potential of the cortical associative memory network it is necessary to consider
the temporal dynamics of neural activation in more detail.
Of course, this has been intensely investigated in the last
30 years, mostly in behaviorally stimulated or activated cortical areas, and there is also considerable work on the statistics of cortical spike trains (e.g. Abeles et al. 1995; Softky
1995; Bair and Koch 1996; Kenet et al. 2003; Knoblauch
and Palm 2005; Renart et al. 2010). For our purpose it suffices to provide a rough qualitative picture of the processes
involved herein. The activity in the axonal fibers of this network consists of spikes and sequences of spikes .The average
spike-frequency will not be very high (e.g. 5 spikes/s; cf. for
example Herz et al. 1964; Burns and Webb 1976 or Renart et
al. 2010), even in an activated area, but this means that still
the number of spikes occurring in the 10,000 afferent fibers to
a typical pyramidal neuron in this network will be 50,000/s,
i.e. 50/ms on average. The corresponding postsynaptic potentials (PSP) will be low-pass filtered and averaged with other
PSPs on their way to the cell-body resulting in a fluctuating signal (with a variance of perhaps 10–20 % of the mean,
depending on the correlation between different spike trains
among other things). Even if the local associative memory
dynamics (of “iterative retrieval”, see Wennekers et al. 1995;
Schwenker et al. 1996) has reached a fixed point in one local
node of the network and the activity would be “constant”
from a computational point of view, there still would be these
fluctuations, and corresponding fluctuations in the timing of
the outgoing spikes generated by these neurons. Our simulations of two cortico-cortically connected areas (Knoblauch
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and Palm 2002a,b or Wennekers et al. 1995) may also give
an impression of this “quasi-constant” fluctuating activity.
Such a relatively constant local activation pattern can persist
for a relatively long time in spite of changes in some of the
inputs from other cortical areas or from outside the cortex.
This may be useful since it is uncertain for how long the
cortico-cortical (or even extra-cortical) inputs activating the
local module can be assumed to be “constant” in this sense.
Despite of these fluctuations we will now make use of
a common theoretical simplification which results in a discretization of neural activity and time: we will consider the
activity reached in one module during this “local settling
time” or LST as one “state” in a simplified computational
description and the LST as the elementary computational
time-step. It is plausible to assume that this “settling” of the
local modules can occur several times per second and this
settling time may well be different for different modules. To
fix ideas we assume here that the LST may be somewhere
between 10 and 50 msec. If we assume that the total travel
time of neural activity from one neuron to its neighbours is
between 1 and 5 msec (e.g., Girard et al. 2001), there can be at
least 3 up to perhaps 30 associative iteration steps in one LST.
We found (Schwenker et al. 1996) that in auto-associative
memory 3 steps are usually enough to reach a “fixed point”,
but of course, the local stabilization of activity could also
lead into a small cycle instead of a fixed point giving room to
some temporal fine structure in the sequence of activation in
a local assembly. In this case, of course, the local associations
learned in the Hebbian synapses would be hetero-associative
between the subsequent patterns of the cycle instead of autoassociative between the neurons in just one pattern (Wennekers and Palm 1996). In each LST step one such pattern
(or small cycle) will move into a subsequent one driven by
the input coming from the cortical input nodes to our local
node. Formally, this can obviously be described as an inputdriven state transition in the local node. So each local node
can be roughly described as a finite automaton (McCulloch
and Pitts 1943; Kleene 1956; Hopcroft and Ullman 1979;
Knoblauch et al 2004; Markert et al. 2005) and the whole
cortex as a network of these automata. We should add here
that the distributed assembly representation of “automatastates” in the local cortical modules provides an important
additional property which intuitively is not machine-like at
all: due to the overlap between different assemblies there is a
notion of similarity between states which may also be used to
influence the state transitions (Palm 1981; Knoblauch et al.
2005a,b; Markert et al. 2007) and there is also the possibility
to represent a superposition of a few states by subthreshold
activity (Knoblauch and Palm 2002a,b).
Theoretically, one reasonably large automaton (provided
with unlimited external memory) can do any kind of computation (Turing 1936; Hopcroft and Ullman 1979), so an
associative memory network of sufficient size (like a human
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Biol Cybern
or monkey or cat cortex) certainly also has this potential.
More importantly, the typical behavioral or cognitive tasks
of an animal or human agent can well be broken down into
processes of matching sensory inputs to learned patterns,
thereby inducing state-transitions that may include outputs
to other areas or even to motor centers of the brain to produce the appropriate reactions (Palm 1982a; Wennekers and
Palm 1996, 2007). Even delayed reactions or longer-term
predictions leading to goal-directed behavior can be learned
in such structures as shown, for example, by the theory of
reinforcement learning, which just requires a simple, biologically plausible learning scheme for the predicted reward
(Sutton and Barto 1998) probably realized in the basal ganglia (Schultz et al. 1997; Schultz 2002), and associative structures that relate the current input to the overall situation,
the expected reward, and a proposed action (Palm 1982a).
Recently we have demonstrated that this associative network structure is also well-suited for simple language understanding and production (Markert and Palm 2006; Markert et
al. 2007, 2008). These more elaborated processing schemes
require more complex temporal considerations which are
paralleled by refined experimental investigations showing
corresponding complex temporal biophysical properties and
mechanisms in the cortex. These more recent developments
are discussed in the next two sections.
From a simplified computational point of view the cortex
can now be regarded as a network of local cortical modules
where the activation in each module is regarded as “approximately constant” i.e. as in one “activity state” (described by a
corresponding pattern of active neurons) for a certain period
of time, which we have called the LST.
Since we cannot assume a global clock which determines
the duration of all LSTs, we need for each local module a
mechanism that determines the end of the current LST and
the switching to the next “state”. In Wennekers and Palm
(2009) we have discussed such mechanisms leading to the
suggestion that states can remain stable for long durations
due to the strong auto-associative internal connectivity in the
local module and that state-transitions can be triggered simply by increasing background excitation (most likely from
the thalamic region that corresponds to the cortical area (e.g.
Jones 1985; Brodal 2010). Again, this state switching dynamics can also be directed into different branches, i.e. branch
to different next states, depending on the specific excitation
from related areas through the A-system. This mechanism
can be used to create variable LSTs in different cortical areas
and to organize their interplay among the nodes in the cortical network according to the current computational demands.
For example, in hierarchical processing of incoming sensory
signals or motor behaviors it may be useful to have longer
LSTs at higher hierarchical levels combining several shorter
LSTs at lower levels. There is actually physiological evidence
that short LSTs are typical for early visual or auditory areas
whereas longer LSTs, which may also be considered as a
realization of working memory, are more pronounced in the
frontal parts of the cortex, where sensory-motor patterns can
perhaps be integrated over larger periods of time (see for
example Huyck and Passmore 2013).
It is hard to create a generic scheme for such a corticothalamo-cortical control system. However, the anatomical
and physiological basis for such a system exists (Miller 1996;
Sherman 2007) and concrete realizations for the task of sentence understanding and also continuous speech recognition
(in the Wall Street Journal corpus) can be found in Markert
et al. (2007, 2009) and Kara and Palm (2008). For this kind
of organization we found it useful and actually sufficient to
have a measure for the total or average local activity in each
module and to use it for thalamic control by other corticocortically related modules (see Bouchain and Palm 2012).
But of course the question, how such a delicate control structure could have developed by a combination of genetic evolution and individual learning still remains a mystery to us.
5 Synaptic plasticity and learning
One basic assumption of our view of the cortex as an organized network of local cortical modules is the use of autoand hetero-associative learning for the stabilization of local
patterns in single modules and the establishment of corticocortical relations between patterns in different modules. The
synaptic mechanism for the formation of these auto- and
hetero-associations was supposed to be Hebbian synaptic
plasticity (point 7, see also Palm 1982a,b).
Over the last twenty years, synaptic plasticity has been
investigated intensely, in particular with respect to the timing of the “coincidence” of pre- and postsynaptic activity.
The most prominent view today concerning synaptic plasticity in the cerebral cortex (including the hippocampus) is that
it is an ubiquitous phenomenon that seems to be triggered
by the timing of the presynaptic spike and the postsynaptic spike that is apparently backpropagated through the dendritic tree of the postsynaptic neuron. This kind of plasticity
is called “spike-timing dependent plasticity” (STDP). The
by now classical figure 7 of Bi and Poo (1998) shows their
experimental findings concerning the increase or decrease
of synaptic effectivity as a function of the time difference
between the occurrences of a pre- and a postsynaptic spike
where the presynaptic spike arrives at the synapse on the
axon of the presynaptic neuron as usual and the spike of the
postsynaptic neuron is backpropagated through the dendritic
tree to the synapse (compare F in Fig. 3, corresponding to
similar data from Froemke and Dan 2002). Interpreting this
finding as evidence for a local mechanism at each individual synapse implies that the two times in question mark the
passing-by of the backpropagated postsynaptic and the presynaptic spike at the synapse. The figure of Bi and Poo shows
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Biol Cybern
that roughly coincident firing of pre- and postsynaptic spikes
will generally tend to increase synaptic strength, but in more
detail, the presynaptic spike should occur a few msec before
the postsynaptic one at the synapse and the reverse temporal
relation occurring repeatedly will lead to a decrease of synap-
a
tic strength (Carporale and Dan 2008). Backpropagation of
spikes through the dendritic tree and STDP mechanisms of
this type are today believed to be ubiquitous not only in the
hippocampus, but throughout the cortex (Kampa and Stuart
2006; Spruston 2008, 2009).
#spikes
population spike activity
STDP on at t=3sec
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syn.strength over delay
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#spike pairs
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t=10sec
2
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post
500
−t
pre
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[msec]
Fig. 2 Network simulation showing that STDP (spike-timing dependent plasticity) can couple neurons that fire in synchrony. a Summed
spike activity of a simulated neuron population as a function of time
(10 ms sliding time window). Initially (t < 3 s), synchronization is
weak. However, synaptic modification by STDP (switched on at t = 3 s)
increases synaptic strength for connections with small axonal transmission delays (panel c) leading to strong synchronized oscillations of
spike activity. Correspondingly, the distribution of time lags between
pre- and postsynaptic spikes gets increasingly peaked (b). Note that the
123
0
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8
delay d [msec]
10
12
effect of STDP increases strongly with the presence of synchronization (e.g., see c: there is only little change in the strength distribution
between t = 0 and t = 10, but a strong change between t = 10 and t = 20,
corresponding to the strong increase of synchronization around t = 13).
Still, the “decoupling effect”, for example, as described by Lubenov
and Siapas (2008) for very precise (stimulation-induced) synchronization, occurs only for synapses with large delays, whereas synapses with
small delays (e.g., d < 4 ms) continue to increase their strengths. Figure
modified from Knoblauch et al. (2012) (color figure online)
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Biol Cybern
a
1.2
b
T=1msec
1.2
1
T=10msec
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STDP function F
0.8
G and F (normalized)
G and F (normalized)
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c
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− tpre
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s
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0.2
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precise sy
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c)
(T=1mse
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mean spike rate λ [spikes/sec]
35
40
Fig. 3 STDP can either couple or decouple synchronized neurons
depending on the distribution of spike time lags G (at the synaptic site)
and the shape of the STDP curve F (from Froemke and Dan 2002). In
general, the resulting expected weight change (per spike) is the integral
of the product of F and G. a Precise synchronization (time window
T = 1 ms) results in depression of synaptic strength even for small effective transmission delays (d = 1 ms) because the lag distribution G has
overlap only with the LTD (long term depression) branch of the STDP
curve F.b More realistic coarse synchronization (T = 10 ms) results in
potentiation of synaptic strength because G overlaps also with the LTP
(long term potentiation) branch of F (that dominates over LTD). c Con-
tour plot of expected weight change (i.e., the integral of FG) as a function
of T and d showing a large parameter region where coarsely synchronized neurons get coupled by LTP. d Average weight change as function of average spike rate for uncorrelated firing (“rate coding”, Black
curve), precise synchronization (T = 1 ms, blue), and coarse synchronization (T = 10 ms, green) assuming d = 1 ms. Note that coarse synchrony is most effective in coupling neurons even at low firing rates.
Effective delay d = d0+dax-dbap includes time shift of the STDP curve
(d0), axonal delay (dax), and dendritic delay of the backpropagating
spike (dbap). Figure modified from Knoblauch et al. (2012) (color figure online)
The finding of Bi and Poo is clearly consistent with the
use of STDP for hetero-association, because the incoming
(cortico-cortical) presynaptic spike pattern will help to activate the postsynaptic local population subsequently. This has
also been shown in simulation studies of STDP (Gerstner
et al. 1993; Levy et al. 2001; Izhikevich 2006; Morrison et
al. 2007). Its use for auto-association, however, seems problematic, because auto-associative connections are between
neurons of the same population which are presumably firing
(roughly) in coincidence, and the axonal delays leading from
the presynaptic cell body to the synapse are probably longer
than the dendritic delays of the postsynaptic spike back to the
synapse. Therefore STDP was generally believed to strongly
depress synaptic strengths of auto-associative connections
which has also been shown in several computer simulations
(Knoblauch and Sommer 2003, 2004; Kozloski and Cecchi
2008, 2010; Lubenov and Siapas 2008; Clopath et al. 2010;
Hauser et al. 2009; Hauser et al. 2010).
Recently, we have repeated these experiments for various
STDP models with biologically realistic parameter ranges
(Knoblauch et al. 2012; Hauser 2012). We found that a reasonable jitter in the occurrence times of the spikes in the
active population can indeed lead to enhancement of the
auto-associative connections even if the axonal delay to the
synapse is a bit longer than the dendritic delay. This is shown
in Figs. 2 and 3.
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Basically, our simulations and analyses reveal that STDP
strengthens the synaptic connections between synchronized
neurons if the jitter of spike times (parameter T in Fig. 3) is
larger than the effective (axonal minus dendritic) transmission delays (parameter d in Fig. 3). This effect can easily
be understood by inspecting shapes of experimental STDP
curves, for example, as measured by Bi and Poo. There, the
discontinuity near zero time lag is typically such that the
synaptic potentiation for small positive time lags is much
larger than the synaptic depression for small negative time
lags (see STDP function F around t=0 in Fig. 3). Thus, averaging over a mixture of potentiation and depression events as
expected for synchronization with realistic spike jitter [e.g.,
10msec range, for more discussion see for example Wennekers and Palm (1999)] will lead to a net potentiation of synaptic
strength even for significant axonal delays and low average
firing rates. We have extended this reasoning also to more
realistic models of STDP, for example based on spike triplets
instead of spike pairs (Pfister and Gerstner 2006; Clopath
et al. 2010). Our results reconcile STDP with the idea that
spike synchronization has a constructive rather than destructive role in the formation of auto-associative memories and
cell assemblies.
6 Conclusion
The 1978-paper by Braitenberg has provided strong arguments for a theory of cell assemblies in the spirit of Donald
Hebb by showing how well the particular structure of the
cerebral cortex fits the requirements of such a theory. This
has been substantiated by the neuroanatomical research over
the last 30 years. As discussed in Sect. 2, a lot of quantitative
data from neuroanatomy have accumulated which—together
with data from physiology (for review see Huyck and Passmore 2013)—make it possible to deal with computational
and dynamical aspects of cell assemblies in an associative
network of cortical areas. This theoretical scheme also fits
well with most of the functional “cortex theories” that have
been developed from Donald Hebb’s early book (Hebb 1949)
up to the present day. Such a theory of the cortex as a network of local networks generated by a combination of genetic
wiring principles and individual associative learning has been
sketched here (and earlier for example by Markert et al. 2007)
exhibiting the enormous computational capabilities of the
cortex for quite general cognitive demands.
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